In this paper, I present an exploratory study on cross-linguistic interference among Quechua-Spanish bilingual children living in a language contact situation. The study focuses on convergence in the tense, aspectual and evidentiality systems of the two languages. While in Quechua past tense features are strongly linked to evidentiality in the matrix of features associated with the functional category Tense, in Spanish, past tense features are linked to aspectual features. The study presents evidence that supports the Functional Convergence Hypothesis according to which syntactic convergence among bilingual speakers is favored when the matrix of features associated with a functional category is partially divergent, as is the case for Tense in Spanish and Quechua. The Spanish results indicate that among bilinguals past tense is associated with evidentiality features and contrast sharply with the results of the monolingual comparison group. Bilingual Quechua results exhibit an incipient emergence of discourse-oriented background and foreground distinctions, similar to those found in Spanish in association with aspectual morphology.